In medical imaging, movements of the body result in blurred images. Especially when long image recording times are required the movements cause significant deterioration of the quality of the images and the images may contain blurred edges. The intensity at the location of objects, whose size is smaller than or about equal to the distance over which the objects move during the recording, is lower than expected. Very small objects may completely disappear in the noise as the result of blur.
A combination of Positron Emission Tomography (PET) scanning with Computer Tomography (CT) scanning, or a combination of PET scanning with Magnetic Resonance Imaging (MRI) scanning, is often used to investigate whether a tumor is malignant or benign. CT scanning and MRI scanning enable a sharp, and often detailed, image of tissues in the investigated area of a body to be obtained in which tumors may be localized. With PET scanning an image is created in which the intensity of the pixels or voxels relate to the concentration of a specific active molecule. A tracer is bound to the active molecule, which makes the active molecule visible in a PET scanner. For example, when glucose with the tracer is applied to a body, after some time the concentration of glucose will be higher in malignant tumors than in benign tumors. Thus, the intensity shown in PET scanning images may relate to the amount of glucose absorbed by a tumor and as such it may relate to the malignancy of the tumor.
Especially PET scanning requires long image recording times. When the lung of a person or animal is investigated, the PET images of the lung area will be subject to a lot of blur, because of the pulmonary movement. The CT scan records the image by obtaining images of slices of the body. Each of the recordings of a slice is relatively short such that each slice may be recorded during a single breath-hold. The absence of the pulmonary movement during CT scanning results in relatively sharp images.
Thus, when pulmonary tumors are investigated with a combined PET-CT/MRI scanner, the size of the tumor may be obtained from CT/MRI images and the malignancy of the tumor may be assessed by inspecting the PET image. However, due to the large amount of blur, the malignancy of small tumors is underestimated.
Today, the nuclear physician may estimate the blur and correct the PET intensity profile of the tumor by hand. Alternatively, the estimation and correction are performed automatically. If the nuclear physician estimates the blur, his estimation is based on experience and in general on images shown along the central axes of the investigated body, or along the image axes of the scanner.
Wiemker R., et al., describe in “Combined motion blur and partial volume correction for computer aided diagnosis of pulmonary nodules in PET/CT” (International Journal of Computer Assisted Radiology and Surgery, volume 3, numbers 1-2, published 27 May 2008) a technique to automatically determine the Point Spread Function (PSF) of the blur. A CT volume image is segmented in order to obtain a shape model of a tumor. The method, disclosed in the cited article, determines the Full Width at Half Maximum (FWHM) value of a Gaussian PSF representing the effect of blur. An isotropic PSF is assumed for the blur. Iteratively different Gaussian PSFs, with varying FWHM values, are convoluted with the shape model of the tumor in order to determine how much the convolution result fits the volume image obtained by a PET scan. The FWHM of the Gaussian PSF which results in most cross-correlation between the convolution result and the volume image of the PET scan, is the width of the Gaussian PSF representing the blur in the PET image. Knowing the width of the Gaussian PSF of the blur allows the correction of the maximum PET intensity value or the correction of the volume image of the PET scan.
The authors of the cited article realized that modeling the effect of blur as an isotropic Gaussian PSF is an oversimplification. The authors propose to model blur as an anisotropic PSF by a 3×3 covariance matrix. Such a 3×3 covariance matrix is symmetrical and contains 6 free parameters which must be determined. However, calculating values for the 6 free parameters results in an algorithm that requires a lot of computation power and the algorithm has problems with respect to robustness and numerical stability.